This is where we will post our past weekly math problems! We post a problem every week around Saturday at noon. We will only have weeks starting at Week 31 of 2022. Click the button for the archive of the rest of the problems.

For every level Kevin completes in his favorite game, he earns 520 points. Kevin already has 200 points in the game and wants to end up with at least 2580 points before he goes to bed. What is the minimum amount of levels Kevin needs to complete to reach his goal?

To solve this, we can set up an equation where x is the amount of levels Kevin needs to complete.

200 + 520x = 2580 where 200 is the starting point and 2580 is the amount of points Kevin wants to finish by the end of the night.

*x*⋅520+200≥2580

*x*⋅520≥2580−200

*x*⋅520≥2380

The minimum amount of levels Kevin needs to complete is 520.

Kevin sells magazine subscriptions and earns $4 for every new subscriber he signs up. Kevin also earns a $33 weekly bonus regardless of how many magazine subscriptions he sells. **If Kevin wants to earn at least **$36** this week, what is the minimum number of subscriptions he needs to sell?**

Since the Amount earned this week =

Subscriptions sold × Price per subscription + Weekly bonus, we can set up an inequality to determine how many we need. Amount sold this week should be equal or greater than 36 which means Subscriptions sold x price per subscription + weekly bonus ≥ 36. We can now plug in: *x*⋅$4+$33≥$36*x*⋅$4≥$36−$33*x*⋅$4≥$3*x*≥34≈0.75 Since Kevin cannot sell parts of subscriptions, we round 0.75 up to 1. **Kevin must sell at least 1 subscriptions this week.**

Divide x3−12x2−42*x*3−12*x*2−42 by x−3*x*−3

See Image on Left

Divide x^3+x^2+x+1 by x+9

See image.

Final answer: x^2 - 8x + 73 - (-656/x+9)

Solve the system of equations using the graph.

See Image on Left

Describe the end behavior of the function to the left.

As x approaches infinity, y approaches infinity.

As x approaches negative infinity, y approaches infinity.

Find the domain of the function f(x) = (x^2) / √x + 2

The domain of the function is D=(-∞,∞) x ≠ -2 since you can't divide over 0.

A school wants to order shirts for homecoming. There is an initial deposit of $150 and $15 per shirt after the deposit. If the school sells the shirts for $20 a piece, how many do they need to sell to make a profit?

This can be represented by a system of equations.

The price of ordering the shirts is y = 15x + 150 where x = the amount of shirts ordered. The amount of money that they would get from selling shirts can be modeled using y=20x where x = the amount of shirts ordered.

These two equations should be equal to each other: 15x + 150 = 20x

150 = 5x

X = 30. The school needs to sell 30 shirts.

The product of (20 1/2)(22 1/4) can be written as A B/C where A, B, and C are whole numbers and B<C. What is A + B + C?

First, you can rewrite the 2 numbers as mixed numbers. This step is optional but will make the multiplication easier.

As a product, I got 3649/8. This written as a mixed number would equal 456 1/8. Therefore A = 456, B = 1, and C = 8. This means that A + B + C = 465.

Compute the 2022nd term of the arithmetic series that begins with 3, 9, 15.

Since this is an arithmetic series, you can use the arithmetic series formula to find the 2022nd term.

an = a + (n – 1)d

a2022 = 3 + (2022 – 1)6

a2022 = 12129

What is the horizontal asymptote of the function:

x = (3x^2 + 3x)/(x + 4)

Since the largest power of the numerator is greater than that of the denominator, there is no horizontal asymptote.

For what x values of the function f(x) = (2x + 4) (x^2 + 4) equal zero?

When x = -(1/2), y = 0. While there are other roots, they are imaginary.

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